Algebra Examples & Exercises

These sites are mentioned elsewhere on this site but these all include notes and exercises on Algebra. Answers are included in these resources and of course you can check answers on WolframAlpha.

Note there are resources for older students further down the page.

For younger students (age 11-16) try the Interactive Tutorials from The Centre for Innovation in Mathematics Teaching, (CIMT).
Fundamental Skills   Function Machines   Linear Equations   Basic Factorising
Expansion – Single Brackets  Linear Equations with Brackets
Factorising Expressions 
Substitution into Formulae 1     Substitution into Formulae 2
Linear Equations 1   Linear Equations 2
Coordinates   Plotting Straight Lines   Graphs and Gradients
Laws of Indices   Negative Indices   Fractional Indices
Straight Line Graphs   Linear Equations   Parallel and Perpendicular Lines
Simultaneous Equations   Equations in Context
Equations, Formulae and Identities   Simplifying Expressions   Factorising  Using Formulae
Quadratic Equations: Factorisation  
and by Completing the Square

The following example – note the colours shows how to expand three brackets.
You could check your answers on WolframAlpha and change the query to make up your own examples.
Expand Brackets Colleen Young

The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with worked solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.

Trinity school (age 11-16)
Trinity School have very helpful Mathematics resources – many examples for you to try (answers included) including Algebra.
Trinity School Nottingham - numerous questions and answers

Trinity School Nottingham – numerous questions and answers

For older students who have already studied many topics in Algebra, CIMT’s Step Up to A Level Maths includes notes and examples on Basic Algebra, Quadratic Functions and Equations and Inequalities. These exercises could also be used by GCSE students aiming for the highest grades. Another very useful publication is the Algebra Refresher from The Mathcentre which has many questions with the answers provided at the end of the document. Also from the Mathcentre you can view all the topics available – several different resource types such as notes and videos are available for each topic.

Sections 1 (Basic Algebra) & 3 (Equations, Inequalities and Partial Fractions) of the very helpful Helm Workbooks include worked examples and exercises (with answers).

Plymouth University Algebraic Fractions

Plymouth University Support Materials

Plymouth University have some very clear workbooks, try Basic Algebra – Brackets for example or Algebraic Fractions.

For videos try the following sites:

Exam Solutions GCSE Maths     

Exam Solutions A Level Maths (select your exam board from A Level Maths tab)

Hegarty Maths GCSE      A Level  and KS3 for younger students (11-14)

and note The Mathcentre, already mentioned above.


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